Steady-state and ultrafast transient absorption spectra were obtained for a series of conformationally constrained, isomerically pure polyenes with 5-23 conjugated double bonds (N). These data and fluorescence spectra of the shorter polyenes reveal the N dependence of the energies of six (1)B(u)(+) and two (1)A(g)(-) excited states. The (1)B(u)(+) states converge to a common infinite polyene li...

Calendrical calculations are ubiquitous. Banks need to calculate interest on a daily basis. Operating systems need to switch to and from daylight savings time. Dates of secular and religious holidays need to be computed for consideration in planning events. Paychecks need to be issued on weekly, biweekly, or monthly schedules. Bills and statements must be generated periodically. Most of these c...

Calculational proofs—proofs by stepwise formula manipulation—are praised for their rigor, readability, and elegance. It seems desirable to reuse this style, often employed on paper, in the context of mechanized reasoning, and in particular, program verification. This work leverages the power of SMT solvers to machine-check calculational proofs at the level of detail they are usually written by ...